The home secretary Theresa May's claim that a Bolivian student was saved from deportation by the existence of a pet cat appears to have been lifted almost word for word from the leader of the UK Independence party.

In her speech to the Tory conference May said the courts, citing the Human Rights Act, had declared the man should not be deported because he would be separated from his cat.

Her remarks led to a spat with the justice secretary, Kenneth Clarke, who accused her of giving a "laughable, childlike" example to criticise the act. Behind the row is a deeper political dispute over whether Britain should ditch the act.

In Manchester this week May matched Farage not just in her phrasing but in her timing when talking about the same immigrant, who she said "cannot be deported because – and I am not making this up – he had a pet cat".

Farage told the Guardian: "I have become increasingly used to the Tory party mimicking our policies and phrases in a desperate effort to pretend to their members they are still Eurosceptic. They don't mean it. We are one of those parties that still believe in holding public meetings, and asking questions from the public. The SWP [Socialist Workers party] turn up, so obviously does Theresa May's speech writers.

"Maybe this will be the beginning of a trend? Flat taxes, cutting foreign aid, a referendum on Europe, grammar schools. Who knows?"

One government member said: "Not only has Ms May been caught out making up stories about the Human Rights Act for cheap laughs, she has been plagiarising her clap lines from the UK Independence party."

The immigrant had avoided deportation after it was ruled that it would breach his right to a family life. In Eastleigh, Farage claimed the incident had occurred a few weeks ago and that the man in question was Peruvian – when he was in fact Bolivian. He also claimed inaccurately that the man had a conviction for manslaughter. Apart from overstaying his visa, he was a law-abiding citizen.

Both politicians inaccurately claimed the man had been granted leave to stay under the Human Rights Act when it was because the tribunal had previously failed to treat his partner as a spouse, which would accord a right of residence.

David Cameron in 2006 earned the ire of Ukip by describing them as "fruitcakes, loonies and closet racists, mostly".

Farage may not have spotted his role as May's speech writer since he has been obsessing about the state of the euro, and the way in which George Osborne, the "British chancellor is telling the rest of Europe it must abandon democracy. It's appalling."